Harnack Estimate for the Endangered Species Equation

Xiaodong Cao; Mark Cerenzia; Demetre Kazaras

doi:10.1090/S0002-9939-2015-12576-2

Harnack Estimate for the Endangered Species Equation

Xiaodong Cao, Mark Cerenzia, Demetre Kazaras

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We prove a differential Harnack inequality for the Endangered Species Equation, which is a nonlinear parabolic equation. Our derivation relies on an idea related to the parabolic maximum principle. As an application of this inequality, we will show that positive solutions to this equation must blow up in finite time.

Original language	English (US)
Pages (from-to)	4537-4545
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	10
DOIs	https://doi.org/10.1090/S0002-9939-2015-12576-2
State	Published - Oct 1 2015
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Differential Harnack inequality
Endangered Species Equation

Access to Document

10.1090/S0002-9939-2015-12576-2

Cite this

@article{a60518e9779e4eaaa230874abef5348a,

title = "Harnack Estimate for the Endangered Species Equation",

abstract = "We prove a differential Harnack inequality for the Endangered Species Equation, which is a nonlinear parabolic equation. Our derivation relies on an idea related to the parabolic maximum principle. As an application of this inequality, we will show that positive solutions to this equation must blow up in finite time.",

keywords = "Differential Harnack inequality, Endangered Species Equation",

author = "Xiaodong Cao and Mark Cerenzia and Demetre Kazaras",

note = "Publisher Copyright: {\textcopyright} 2015 American Mathematical Society.",

year = "2015",

month = oct,

day = "1",

doi = "10.1090/S0002-9939-2015-12576-2",

language = "English (US)",

volume = "143",

pages = "4537--4545",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "10",

}

TY - JOUR

T1 - Harnack Estimate for the Endangered Species Equation

AU - Cao, Xiaodong

AU - Cerenzia, Mark

AU - Kazaras, Demetre

PY - 2015/10/1

Y1 - 2015/10/1

N2 - We prove a differential Harnack inequality for the Endangered Species Equation, which is a nonlinear parabolic equation. Our derivation relies on an idea related to the parabolic maximum principle. As an application of this inequality, we will show that positive solutions to this equation must blow up in finite time.

AB - We prove a differential Harnack inequality for the Endangered Species Equation, which is a nonlinear parabolic equation. Our derivation relies on an idea related to the parabolic maximum principle. As an application of this inequality, we will show that positive solutions to this equation must blow up in finite time.

KW - Differential Harnack inequality

KW - Endangered Species Equation

UR - http://www.scopus.com/inward/record.url?scp=84935017908&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84935017908&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2015-12576-2

DO - 10.1090/S0002-9939-2015-12576-2

M3 - Article

AN - SCOPUS:84935017908

SN - 0002-9939

VL - 143

SP - 4537

EP - 4545

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 10

ER -

Harnack Estimate for the Endangered Species Equation

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this